One of the political fliers features two burning cigarettes beneath the ominous words: “Steve Glazer’s Big Tobacco Problem.” Below are cryptic warnings: “F Rating from the American Lung Association” and “$334,000 in Tobacco Money.”

In another variation on the theme, a nurse stares solemnly into the camera with a thought bubble nearby: “Every day I witness the suffering caused by cigarettes. Steve Glazer is too cozy with the tobacco industry.”

Maybe the most eye-catching effort is a bit of photo gimmickry that shows Glazer’s head peeking out of a torso made entirely of cigarette butts.

“That’s my family’s favorite,” Glazer said sarcastically.

Welcome to the world of mudslinging politics, blatantly misleading claims and one of the costliest races in the June primary election: the 16th Assembly District. Four candidates are competing for two spots in the general election, but most of the $2.8 million dollars already spent on the race involve moderate Democrat Glazer, an Orinda city councilman, and liberal Democrat Tim Sbranti, the mayor of Dublin.

They represent the opposite ends of the same party — one tilting toward business, the other hitched to labor. Glazer is backed by the state Chamber of Commerce, Sbranti by teachers and state workers unions. But Sbranti’s backers, identified as Californians for Economic Prosperity (who’s not for that?) clearly are better at outlandish accusations.

Those alleged ties to tobacco relate to Glazer’s one-year stint as a consultant for JobsPAC, an action committee for California employers, which has indeed received funding from Philip Morris. It’s also received funding from Safeway, Enterprise Rent-a-Car and Blue Diamond Growers, but those aren’t as damning as a tobacco company.

“I’ve never taken a dime from the tobacco industry for this or any other campaign,” Glazer said, explaining that he was hired to help Democratic candidates Mark Levine of San Rafael and Richard Bloom of Santa Monica in their 2012 Assembly races. Both won, and one of Levine’s first bills (AB746) banned smoking in multifamily dwellings. So much for Glazer’s cozy ties to tobacco.

Sbranti takes no ownership of the hit pieces — 10 mailers of similar ilk and one TV spot — distributed in the last month by Californians for Economic Prosperity. (“I’m not involved in that in any way,” he said. “It’s an independent campaign.”) The mailers also accuse Glazer of taking money from oil and insurance companies, apparently by the same logic.

About that “F” from the American Lung Association? It refers to the organization’s annual tobacco-control report card for which Orinda, where Glazer serves, received a failing grade. So did Moraga, Brentwood, El Cerrito, Pittsburg and Antioch. So don’t vote for anyone from those cities, either.

“Smoking has never been an issue in our city,” Glazer said. “I’ve been on the council for 10 years, and I’ve never heard anyone say we have a problem.”

Negative campaigning is not a one-way street here. A mailer on Glazer’s behalf accuses Sbranti of reducing the Dublin police force and cutting library spending. And Glazer is just as well-heeled as his opponent. This is politics; both are big boys, and a lot is at stake. But distortions of fact have no place in the race.

“I think the voters are going to wade through all this, look at our records and our backgrounds and make a decision,” Sbranti said.